How to transmit uv and texture when using Tissue
With the small part of the mesh selected apply scale and rotation and unwrap the image.

Take a mesh that tissue is going to apply (i have taken a cube and subdivide few times)

Select the small mesh and hold shift and click Cube and click on tessellate in tool shelf

Now we got the new shape of the mesh from the Addon with no material and no uv applied to it. Go to edit mode and select all faces and Press Ctrl+N (flip Normal)

In the Edit mode Press L key on one face which select the small part of the mesh.

With the small face selected Press Shift+G -> Area

And now the complete mesh is selected

Press U to unwrap

And apply material on to it.